SUMMARY
The discussion focuses on evaluating the expression $m^4-18m^2-8m$, where $m=\sqrt{p}+\sqrt{q}+\sqrt{r}$ and $p,\,q,\,r$ are the roots of the polynomial $x^3-9x^2+11x-1=0$. The roots can be determined using Vieta's formulas, which provide relationships between the coefficients and the roots of the polynomial. The evaluation of the expression involves substituting the calculated value of $m$ into the polynomial expression.
PREREQUISITES
- Understanding of polynomial roots and Vieta's formulas
- Knowledge of algebraic manipulation of expressions
- Familiarity with square roots and their properties
- Basic skills in evaluating polynomial expressions
NEXT STEPS
- Study Vieta's formulas in depth to understand relationships between polynomial coefficients and roots
- Learn techniques for manipulating and simplifying algebraic expressions
- Explore methods for finding roots of cubic polynomials
- Practice evaluating complex polynomial expressions with multiple variables
USEFUL FOR
Students and educators in mathematics, particularly those focusing on algebra and polynomial equations, as well as anyone interested in advanced algebraic techniques and evaluations.